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Geometry of Prym semicanonical pencils and an application to cubic threefolds

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In the moduli space $\mathcal{R}_{\mathrm{g}}$ of double étale covers of curves of a fixed genus $g$, the locus formed by covers of curves with a semicanonical pencil consists of two irreducible divisors $\mathcal{T}_g{ }^e$ and $\mathcal{T}_g^o$. We study the Prym map on these divisors, which shows significant differences between them and has a rich geometry in the cases of low genus. In particular, the analysis of $\mathcal{T}_5^o$ has enumerative consequences for lines on cubic threefolds.

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Geometry of Prym semicanonical pencils and an application to cubic threefolds